Model based estimation of a complete or partial positron emission tomography attenuation map using maximum likelihood expectation maximization

ABSTRACT

Example embodiments are directed to a method of correcting attenuation in a magnetic resonance (MR) scanner and a positron emission tomography (PET) unit. The method includes acquiring PET sinogram data of an object within a field of view of the PET unit. The method further includes producing an attenuation map based on a maximum likelihood expectation maximization (MLEM) of a parameterized model instance and the PET sinogram data.

FIELD

Example embodiments relate to methods for estimating an attenuation mapin a positron emission tomography and magnetic resonance system(MR-PET).

BACKGROUND

Positron emission tomography (PET) is being used alongside magneticresonance tomography (MR) in medical diagnostics. While MR is an imagingmethod for representing structures and slices inside the body, PETallows in vivo visualization and quantification of metabolic activities.

PET uses special properties of positron emitters and positronannihilation in order to quantitatively determine the function of organsand/or cell regions. With this technique, appropriateradiopharmaceuticals marked with radionuclides are administered to thepatient prior to the examination. As they decay, the radionuclides emitpositrons which after a short distance interact with an electron,causing annihilation to occur. This results in two gamma quanta whichfly apart in opposite directions (offset by 180°). The gamma quanta aredetected by two opposing PET detector modules within a specific timewindow (coincidence measurement), as a result of which the annihilationsite is localized to a position on the line connecting said two detectormodules.

In the case of PET, the detector module generally covers a greater partof a gantry arc length for the purpose of detection. The detector moduleis subdivided into detector elements having a side length of a fewmillimeters. On detecting a gamma quantum, each detector elementgenerates an event record that specifies the time and the detectionlocation. This information is passed to a fast logic unit and compared.If two events coincide within a maximum time interval, it is assumedthat a gamma decay process is taking place on the connecting linebetween the two associated detector elements. The PET image isreconstructed using a tomography algorithm, for example, backprojection.

In a PET system, such as an MR-PET system, the gamma quanta areattenuated by anything situated between the site of origin of therespective gamma quanta and the PET detector. The attenuation must betaken into account in the reconstruction of PET images in order toprevent image artifacts. Situated between the site of origin of thegamma quantum in the patient's body and the acting PET detector areobjects such as tissue within the patient's body, air, and a part of theMR/PET system itself, for example, a patient positioning table. Theattenuation values of the objects between the site of origin of thegamma quantum and the acting PET detector are taken into account andcompiled into attenuation maps (p maps).

An attenuation map contains attenuation values for each volume element(voxel) of the volume under examination. Thus, for example, anattenuation map can be produced for the patient positioning table. Thesame applies to, for instance, local coils attached to the patient forMR examinations. In order to produce the attenuation map, theattenuation values are determined and combined. They can be determinedby means of, for example, a CT recording or PET transmission measurementof the respective component. Attenuation maps of said kind can bemeasured on a once-only basis, since the attenuation values do notchange over the life of the respective component.

Methods are known by which attenuation values of the patient's body canbe determined from anatomical MR images and can be added to theattenuation map. In this case special MR sequences are used by means ofwhich different attenuating tissue classes (e.g., lung tissue), forexample, can be identified. With the aid of the MR images it is thenpossible, based on the position of the attenuating tissue class, toassign appropriate attenuation values to the attenuation map.

However, a transaxial MR field of view is generally smaller than the PETfield of view. Therefore, a portion of an object to be examined is onlyin the PET field of view. Consequently, obtaining attenuation valuesoutside the MR field of view becomes difficult.

MR based estimation of a PET attenuation map may be done either bysegmenting the MR image into different tissue types and assigningcorresponding attenuation values to the different tissue types. However,this approach does not address the scanned areas outside of the MR fieldof view.

Recently, maximum-likelihood expectation maximization (MLEM algorithms)has been used to simultaneously reconstruct emission and attenuationmaps from PET sinogram data. The PET sinogram data may be referred to asPET raw data, PET counts or PET count data. The term “image” is an imagereconstructed from the PET sinogram data. An attenuation map from an MRbased segmentation or another known method can be used to initialize theMLEM algorithm.

Other approaches for MR based attenuation correction include the use ofan atlas, model or reference image with a known attenuation such as acoregistered corresponding CT, PET transmission image or body contoursderived from optical 3D scanning. The actual MR image is then registeredto the atlas or reference with known attenuation and the actualattenuation map is deduced from the registration information andadditional post-processing methods.

SUMMARY

Example embodiments are directed to model based estimation of a completeor partial PET attenuation map using MLEM.

At least one example embodiment discloses a method of correctingattenuation in a MR scanner and a PET unit. The method includesacquiring PET sinogram data of an object within a field of view of thePET unit and producing an attenuation map based on a maximum likelihoodexpectation maximization (MLEM) of a parameterized model instance andthe PET sinogram data.

At least another example embodiment provides for a method of correctingattenuation in a MR scanner and a PET unit. The method includesacquiring PET sinogram data of an object within a field of view of thePET unit and acquiring MR data of the object within a field of view ofthe MR scanner. An attenuation map is produced based on a maximumlikelihood expectation maximization (MLEM) of a parameterized modelinstance and the PET sinogram and MR data. The MLEM is constrained bymodel parameters of the parameterized model instance.

Another example embodiment provides for an apparatus including apositron emission tomography (PET) unit having a plurality of detectionunits and configured to acquire PET sinogram data of an object within afield of view of the PET unit. A magnetic resonance (MR) scanner isconfigured to acquire MR data of the object within a field of view ofthe MR scanner. A computer is configured to produce an attenuation mapbased on a maximum likelihood expectation maximization (MLEM) of aparameterized model instance and the acquired PET sinogram and MR data,the MLEM being constrained by model parameters of the parameterizedmodel instance.

BRIEF DESCRIPTION OF THE DRAWINGS

Example embodiments will be more clearly understood from the followingdetailed description taken in conjunction with the accompanyingdrawings. FIGS. 1-4 represent non-limiting, example embodiments asdescribed herein.

FIG. 1 illustrates a device for superimposed MR and PET imagerepresentation that may be used in the example embodiments;

FIG. 2 illustrates a method of estimating a complete PET attenuation mapusing MLEM to reconstruct a PET image according to an exampleembodiment;

FIG. 3 illustrates a method of estimating a complete PET attenuation mapusing an MR based attenuation map and MLEM to reconstruct a PET imageaccording to an example embodiment; and

FIG. 4 illustrates a method of refining an initial attenuation map usingMLEM according to an example embodiment.

DETAILED DESCRIPTION

Various example embodiments will now be described more fully withreference to the accompanying drawings in which some example embodimentsare illustrated. In the drawings, the thicknesses of layers and regionsmay be exaggerated for clarity.

Accordingly, while example embodiments are capable of variousmodifications and alternative forms, embodiments thereof are shown byway of example in the drawings and will herein be described in detail.It should be understood, however, that there is no intent to limitexample embodiments to the particular forms disclosed, but on thecontrary, example embodiments are to cover all modifications,equivalents, and alternatives falling within the scope of the exampleembodiments. Like numbers refer to like elements throughout thedescription of the figures.

It will be understood that, although the terms first, second, etc. maybe used herein to describe various elements, these elements should notbe limited by these terms. These terms are only used to distinguish oneelement from another. For example, a first element could be termed asecond element, and, similarly, a second element could be termed a firstelement; without departing from the scope of example embodiments. Asused herein, the term “and/or” includes any and all combinations of oneor more of the associated listed items.

It will be understood that when an element is referred to as being“connected” or “coupled” to another element, it can be directlyconnected or coupled to the other element or intervening elements may bepresent. In contrast, when an element is referred to as being “directlyconnected” or “directly coupled” to another element, there are nointervening elements present. Other words used to describe therelationship between elements should be interpreted in a like fashion(e.g., “between” versus “directly between,” “adjacent” versus “directlyadjacent,” etc.).

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of exampleembodiments. As used herein, the singular forms “a,” “an” and “the” areintended to include the plural forms as well, unless the context clearlyindicates otherwise. It will be further understood that the terms“comprises,” “comprising,” “includes” and/or “including,” when usedherein, specify the presence of stated features, integers, steps,operations, elements and/or components, but do not preclude the presenceor addition of one or more other features, integers, steps, operations,elements, components and/or groups thereof.

Spatially relative terms, e.g., “beneath,” “below,” “lower,” “above,”“upper” and the like, may be used herein for ease of description todescribe one element or a relationship between a feature and anotherelement or feature as illustrated in the figures. It will be understoodthat the spatially relative terms are intended to encompass differentorientations of the device in use or operation in addition to theorientation depicted in the Figures. For example, if the device in thefigures is turned over, elements described as “below” or “beneath” otherelements or features would then be oriented “above” the other elementsor features. Thus, for example, the term “below” can encompass both anorientation which is above as well as below. The device may be otherwiseoriented (rotated 90 degrees or viewed or referenced at otherorientations) and the spatially relative descriptors used herein shouldbe interpreted accordingly.

It should also be noted that in some alternative implementations, thefunctions/acts noted may occur out of the order noted in the figures.For example, two figures shown in succession may in fact be executedsubstantially concurrently or may sometimes be executed in the reverseorder, depending upon the functionality/acts involved.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which example embodiments belong. Itwill be further understood that terms, e.g., those defined in commonlyused dictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art andwill not be interpreted in an idealized or overly formal sense unlessexpressly so defined herein.

Portions of the example embodiments and corresponding detaileddescription are presented in terms of software, or algorithms andsymbolic representations of operation on data bits within a computermemory. These descriptions and representations are the ones by whichthose of ordinary skill in the art effectively convey the substance oftheir work to others of ordinary skill in the art. An algorithm, as theterm is used here, and as it is used generally, is conceived to be aself-consistent sequence of steps leading to a desired result. The stepsare those requiring physical manipulations of physical quantities.Usually, though not necessarily, these quantities take the form ofoptical, electrical, or magnetic signals capable of being stored,transferred, combined, compared, and otherwise manipulated. It hasproven convenient at times, principally for reasons of common usage, torefer to these signals as bits, values, elements, symbols, characters,terms, numbers, or the like.

In the following description, illustrative embodiments will be describedwith reference to acts and symbolic representations of operations (e.g.,in the form of flowcharts) that may be implemented as program modules orfunctional processes include routines, programs, objects, components,data structures, etc., that perform particular tasks or implementparticular abstract data types and may be implemented using existinghardware. Such existing hardware may include one or more CentralProcessing Units (CPUs), digital signal processors (DSPs),application-specific-integrated-circuits, field programmable gate arrays(FPGAs) computers or the like.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise, or as is apparent from the discussion,terms such as “processing” or “computing” or “calculating” or“determining” of “displaying” or the like, refer to the action andprocesses of a computer system, or similar electronic computing device,that manipulates and transforms data represented as physical, electronicquantities within the computer system's registers and memories intoother data similarly represented as physical quantities within thecomputer system memories or registers or other such information storage,transmission or display devices.

Note also that the software implemented aspects of the exampleembodiments are typically encoded on some form of program storage mediumor implemented over some type of transmission medium. The programstorage medium may be magnetic (e.g., a floppy disk or a hard drive) oroptical (e.g., a compact disk read only memory, or “CD ROM”), and may beread only or random access. Similarly, the transmission medium may betwisted wire pairs, coaxial cable, optical fiber, or some other suitabletransmission medium known to the art. The example embodiments are notlimited by these aspects of any given implementation.

The term model may mean any kind of attenuation atlas, anatomicalattenuation model, attenuation reference image of an object, or anyother reference used to estimate a PET attenuation map. Moreover, adeformable model may be implemented which may capture all reasonableshapes of an attenuating object and capture all possible attenuationvalues at respective spatial positions. The deformable model may vary inshape and appearance.

The term attenuation appearance model of a model refers to thecollection of all possible attenuation coefficients at a spatialposition within an object such that each spatial position may have a setof potential attenuation coefficients that may occur. An instance of theattenuation appearance model is a specific setting of attenuationcoefficients, one for each spatial position of the object.

FIG. 1 shows a device 1 for superimposed MR and PET image representationthat may be used in the example embodiments. The device 1 includes aknown MR scanner 2. The MR scanner 2 defines a longitudinal direction zthat extends orthogonally to the drawing plane of FIG. 1.

As shown in FIG. 1, a PET unit having a plurality of PET detection units3 arranged in opposing pairs about the longitudinal direction z isdisposed coaxially inside the MR scanner 2. The PET detection units 3include an APD photodiode array 5 preceded by an array of cerium dopedlutetium orthosilicate (LSO) crystals 4 and an electrical amplifiercircuit (AMP) 6. However, example embodiments are not limited to the PETdetection units 3 having the APD photodiode array 5 preceded by an arrayof LSO crystals 4, but other kinds of photodiodes, crystals and devicescan equally be used for detection purposes.

Image processing for superimposed MR and PET image representation isperformed by a computer 7.

Along its longitudinal direction z, the MR scanner 2 defines acylindrical first field of view. The plurality of PET detection units 3defines, along the longitudinal direction z, a cylindrical second fieldof view. According to example embodiments, the second field of view ofthe PET detection units 3 essentially coincides with the first field ofview of the MR scanner 2. This is implemented by appropriately adaptingthe arrangement density of the PET detection units 3 along thelongitudinal direction z.

FIG. 2 illustrates a method of estimating a complete PET attenuation mapusing MLEM to reconstruct a PET image. The MLEM may be any known MLEM.The method of FIG. 2 may be implemented in any PET device or hybriddevice with PET modality such as the device 1 illustrated in FIG. 1.

As shown in FIG. 2, a statistical model is generated at S200. While astatistical model is used for illustrative purposes, it should beunderstood that any other model that may be parameterized may be used inother example embodiments.

The statistical model may be built by performing principal componentanalysis of deformation fields and attenuation maps resulting fromcoregistrations of data sets. Data sets may be obtained from scans ofmultiple individuals and either simple attenuation maps or,corresponding pairs of MR image data and an image from which anattenuation map can be induced (e.g., MR and CT image pairs from eachindividual). By coregistering data sets, statistical variations of ashape (e.g., an arm) and attenuation values may be captured. Principalcomponent analysis allows for a more compact representation of theparameter space to be developed.

Principal components may be obtained from principal axis transformationsof a covariance matrix of input data such as deformation parameters andattenuation parameters. The principal components are the principal Eigenvectors of the covariance matrix of the input data. Transforming theinput data to the principal axis produces a compact linearrepresentation of the input data, from which new instances of the modelcan be generated by linear combinations. Varying linear combinationcoefficients of the principal components produce other instances of thestatistical model.

It should be understood that statistical analysis methods other thanprincipal component analysis, such as clustering analysis, may be usedto reduce dimensionality.

The statistical model may be of the complete body or of any arbitrarybody part. For example, the statistical model may be a kinematic armmodel in combination with an attenuation map of human arms or astatistical atlas and statistical attenuation map of the complete body,for example. The statistical model may be similar to the model describedin Rueckert et al. “Automatic Construction of 3D Statistical DeformationModels Using Non-rigid Registration.” Lecture Notes in Computer Science,vol. 2208 (2001), 77-84 or Fenchel et al. “Automatic Labeling ofAnatomical Structures in MR FastView Images Using a Statistical Atlas.”Lecture Notes in Computer Science, vol. 5241 (2008), 576-84, except thatthese models are based on grey value images instead of attenuation maps.

The statistical model is parameterized by deformation parameters d_(i)and attenuation appearance parameters a_(i) for each instance i. Thedeformation parameters d_(i) parameterize the shape of the object. Theattenuation appearance parameters a_(i) parameterize the attenuationcoefficients at the spatial positions. Examples of attenuationappearance parameters a_(i) are attenuation values of different tissuetypes at their respective spatial position at 511 keV, for example, lungtissue attenuation 0.018/cm.

Both the deformation parameters and the attenuation appearanceparameters are obtained from the coregistered data sets. The covariancematrix over all input instances is then computed. From covariancematrices of the parameters, principal components are extracted. Aninstance of the statistical model can then be described by a linearmodel:

$\begin{matrix}{\mu = {\sum\limits_{i = 0}\left( {p_{i}*w_{i}} \right)}} & (1)\end{matrix}$where μ is the instance of the statistical model, p_(i) are theprincipal components and w_(i) is the coefficient for the i-th principalcomponent in the linear equation. Generally, the coefficients areselected from an interval of three sigma of the principal values. Thecoefficients w_(i) may be the deformation parameters d_(i) for 1<i<m andw_(i) may be the attenuation appearance parameters a_(i) for m+1<i<n.

Therefore, arbitrary instances may be created by assigning differentcoefficients. While the example embodiment of generating andparameterizing a statistical model is described above, it should beunderstood that other methods may be used for other models.

Affine parameters A_(i), including spatial transformation parameterslike such as rotation and translation, may be used to arbitrarily alignand scale the statistical model in space. Moreover, A_(i) can be used tosetup a matrix M and a translation vector t by which each spatialposition may be transformed to:A(x)=M*x+t  (2)after deformation, where x is a vector of a spatial position.

It should be understood that the statistical model may be parameterizedby other parameters instead of, or, in addition to the deformationparameters, the attenuation appearance parameters and the affineparameters.

Based on the statistical model, a PET attenuation map given by the modelinstance μ is created at S210 (e.g., an average model). The PETattenuation map given by the model instance μ may be estimated by thecomputer. More specifically, the attenuation map for the model instanceμ may be a function of d_(i), a_(i) and A_(i) and is defined as:μ(d_(i),a_(i),A_(i))  (3)

L is a log likelihood of an emission image (emitter distribution) L(λ,μ)where λ is an emission image (the spatial distribution of the positronemission). The emission image λ is based on an initial emitterdistribution image that is computed from PET sinogram data, for example,by back projection. The attenuation map given by the model instance μ isa function of the deformation parameters d_(i) and the attenuationappearance parameters a_(i) the affine parameters A_(i), as shown above.Therefore,(λ, μ (d _(i) ,a _(i) ,A _(i)))=arg max (L(λ, μ (d _(i) ,a _(i) ,A_(i))))  (4)becomes the parameter setting for the maximum likelihood. Furthermore,it should be understood that the emission image λ may also beparameterized by a model, for example, the statistical model. Moreover,it should be understood that other measures may be integrated into anextended likelihood. For example, if a statistical distribution of themodel parameters is known or can be approximated, the likelihood of themodel instance itself could be integrated into the likelihood measure.

The larger the amount of data sets, the more comprehensive thestatistical model will be and thus, the more generalized the statisticalmodel will be. It should be understood that the statistical model is apossible embodiment of a deformable model and that each instance i ofthe statistical model is a function of the model parameters for thatinstance. For example, the deformation parameters d_(i) and theattenuation appearance parameters a_(i) the affine parameters A_(i) aremodel parameters.

PET sinogram data of an object within a field of view of a PET unit isacquired at S215. The PET sonogram data may be acquired by the PET unitshown in FIG. 1. Based on the PET sinogram data, the emission image λ(PET image) is computed simultaneously with the model parameters.Alternatively, the emission image λ and the statistical model may becomputed alternatively by first keeping the emission image λ fixed andupdating the statistical model, then keeping the statistical model fixedand updating the emission image.

The emission image λ and the model parameters for that instance areoptimized at S220 based on the PET sinogram data. The emission image λand the model parameters for that instance are optimized in an iterativefashion. During optimization, the emission image λ is computed, thestatistical model is updated and the emission image λ is recomputeduntil optimization has been reached. The model parameters may be thedeformation parameters d_(i), the attenuation parameters a_(i) and theaffine parameters A_(i).

At S220, the PET attenuation map given by the model instance μ and theemission image λ are reconstructed simultaneously based on a MLEMfunction. The computer shown in FIG. 1 may reconstruct the emissionimage λ and the PET attenuation map given by the model instance μ. Theemission image λ and the PET attenuation map given by the model instanceμ may be reconstructed and optimized based on the log-likelihood of the(un-truncated) measured PET emission which is defined as follows:

$\begin{matrix}{{L\left( {\lambda,{\mu\left( {d_{i},a_{i},A_{i}} \right)}} \right)} = {\sum\limits_{i = 0}\left( {{y_{1}*{\log\left( y_{i}^{\prime} \right)}} - y_{1}^{\prime}} \right)}} & (5)\end{matrix}$where y_(i) is the measured PET sinogram data and y_(i)′ is theestimated y_(i) value. y_(i)′ is estimated by forward projecting theemission image λ and correcting attenuation by the attenuation map givenby the model. L can then be optimized as a function of the parametersd_(i), a_(i) and A_(i) and λ. Here, constraining the MLEM to theparameter space of the model is used to estimate the completeattenuation map. The parameter space means all possible values of theparameterized statistical attenuation model. In the example embodimentshown in FIG. 2, the parameter space may include all model parameters,for example, all deformation, attenuation appearance and affinetransformation parameters.

The model parameters are optimized in an iterative fashion until amaximum likelihood has been reached. The optimum can be found by anycommon optimization algorithm. The optimum is the parameter setting forwhich the maximum likelihood reaches a maximum value. The optimumdefines the most likely instance of the parameterized model forattenuation and emitter image.

When the optimization algorithm at S220 has converged, the optimummaximum likelihood has been reached. The attenuation map is thenobtained directly from the model instance and the PET image from theemission image at S225. It should be understood that the emission imageobtained at S225 may be discarded when another PET image reconstructionis triggered using the attenuation map.

FIG. 3 illustrates a method of estimating a complete PET attenuation mapusing an MR based attenuation map and MLEM to reconstruct a PET imageaccording to an example embodiment. The method of FIG. 3 may beimplemented in any PET device or hybrid device with PET modality such asthe device 1 illustrated in FIG. 1.

As shown in FIG. 3, a statistical model is generated at S300. S300 isthe same as S200. Therefore, a detailed description of S300 will beomitted for the sake of clarity and brevity.

At S305 a, an object is scanned by an MR unit within the field of viewof the MR unit to acquire MR data. The MR scanner shown in FIG. 1 may beused to acquire the MR data.

Once the object is scanned, an MR based attenuation map is produced atS305 b. The MR based attenuation map may be generated by any knownmethod of generating an MR based attenuation map and may be produced bythe computer shown in FIG. 1.

Based on the MR based attenuation map and the statistical model, a PETattenuation map for a model instance μ is created at S310. S310 is thesame as S210, except that the PET attenuation map for the model instanceμ is constrained by the MR based attenuation map. Therefore, a detaileddescription of S310 will be omitted for the sake of clarity and brevity.

PET sinogram data of an object within a field of view of a PET unit isacquired at S315. S315 is the same as S215.

At S320, the model parameters for the instance are optimized. S320 isthe same as S220. The model parameters are optimized until a maximumlikelihood has been reached.

Once a maximum likelihood of the PET attenuation map for the modelinstance μ and the emission image λ has been reached, the attenuationmap for the model instance μ defines an optimal attenuation map for themodel instance μ at S325. The reconstructed PET image is also producedat S325, but may be discarded when the optimal attenuation map for themodel instance μ can be used in another reconstruction process to obtaina PET image. Methods of combining MR based attenuation maps and PETattenuation maps are known in the art. Therefore, for the sake ofclarity and brevity, they will not be discussed.

FIG. 4 illustrates a method of refining an initial attenuation map usingMLEM according to an example embodiment. The method of FIG. 4 may beimplemented in any PET device or hybrid device with PET modality such asthe device 1 illustrated in FIG. 1. As shown in FIG. 4, at S400, astatistical model is generated in the same mariner as in FIGS. 2 and 3.

At S402, the statistical model being parameterized is adapted to aninitial attenuation map. The initial attenuation map may be generatedbeforehand from a low-resolution MR image or a transmission scan, forexample. In another example embodiment, a parameterized model thatincludes anatomy which frequently extends outside a MR field of view(e.g., a kinematic model of the human arms) may be added to the initialattenuation map or may be used to complete the initial attenuation map.

At S405, an object is scanned by an MR unit within the field of view ofthe MR unit to produce an MR image. At S410, a model instance iscreated. The model instance is created based on a best fit of theinitial attenuation map with respect to a least squares approach. Forstatistical models, the best fit may be computed by performing anorthogonal projection of the initial attenuation map to the linear spaceof the statistical model, for example. Thus, the model that is createdis an average instance of the statistical model scaled to the initialattenuation map.

At S415, PET sinogram data is scanned and then the model parameters ofthe attenuation map for the model instance μ are optimized at S420. S415and S420 are the same as S215 and S220, respectively. Therefore, S415and S420 will not be described in greater detail, for the sake ofclarity and brevity. At S420, the initial attenuation map is refinedusing MLEM.

At S425, a refined attenuation map is produced based on the maximumlikelihood of the attenuation map for the model instance μ. A PET imageis also produced.

As described above, the methods may be used for estimating a completeattenuation map of an object based on a model using MLEM reconstructionand/or to complete missing parts of an attenuation map which is computedwith other methods before by means of a model. Moreover, the exampleembodiments may be used for refining an attenuation map such asattenuation maps computed from MR-based attenuation map computationmethods including initialization of the model and refinement to thedata. The example embodiments aid in avoiding local maxima and generatevalid and meaningful instances of a model within its parameter space,atlas or reference image.

Example embodiments being thus described, it will be obvious that thesame may be varied in many ways. Such variations are not to be regardedas a departure from the spirit and scope of the example embodiments, andall such modifications as would be obvious to one skilled in the art areintended to be included within the scope of the example embodiments.

1. A method of correcting attenuation in a magnetic resonance (MR)scanner and a positron emission tomography (PET) unit, the methodcomprising: acquiring PET sinogram data of an object within a field ofview of the PET unit; and producing an attenuation map based on amaximum likelihood expectation maximization (MLEM) of a parameterizedmodel instance and the PET sinogram data.
 2. The method of claim 1,further comprising: acquiring MR data of an object within a field ofview of the MR scanner; and producing a first attenuation map based onthe acquired MR data.
 3. The method of claim 2, wherein the producingthe attenuation map includes producing the first attenuation map and asecond attenuation map.
 4. The method of claim 3, wherein the secondattenuation map provides maximum likelihood of the PET sinogram datawithin a field of view of the PET unit including all parts not withinthe field of view of the MR scanner.
 5. The method of claim 1, whereinthe producing the attenuation map includes, generating a model,parameterizing the model by model parameters, and creating theparameterized model instance based on the acquired PET sinogram data andthe parameterized model.
 6. The method of claim 5, wherein the model isa statistical model.
 7. The method of claim 6, wherein theparameterizing the statistical model includes parameterizing thestatistical model by deformation parameters, attenuation parameters andaffine parameters.
 8. The method of claim 6, wherein the generating thestatistical model includes performing principal component analysis ofdeformation fields and attenuation maps resulting from coregistrationsof example data sets.
 9. The method of claim 1, wherein the producingthe attenuation map includes, generating a model, and adapting the modelto an initial attenuation map, the parameterized model instance beingcreated based on the adapted model.
 10. The method of claim 1, whereinthe PET unit is configured to acquire the PET sinogram data.
 11. Themethod of claim 1, wherein a computer connected to the MR scanner andthe PET unit is configured to produce the attenuation map.
 12. Anon-transitory computer-readable medium, when run on a computer,configured to instruct the computer to perform the method of claim 1.13. A method of correcting attenuation in a magnetic resonance (MR)scanner and a positron emission tomography (PET) unit, the methodcomprising: acquiring PET sinogram data of an object within a field ofview of the PET unit; acquiring MR data of the object within a field ofview of the MR scanner; producing an attenuation map based on a maximumlikelihood expectation maximization (MLEM) of a parameterized modelinstance and the acquired PET sinogram and MR data, the MLEM beingconstrained by model parameters of the parameterized model instance. 14.The method of claim 13, wherein the producing the attenuation mapincludes producing a PET attenuation map.
 15. The method of claim 14,wherein the producing the PET attenuation map includes, generating amodel, parameterizing the model by the model parameters, and creatingthe parameterized model instance based on the parameterized model. 16.The method of claim 15, wherein the model is a statistical model. 17.The method of claim 16, wherein the model parameters are the deformationparameters and the attenuation appearance parameters.
 18. The method ofclaim 17, wherein the model parameters further include affineparameters.
 19. The method of claim 14, further comprising: producing anMR attenuation map.
 20. The method of claim 13, wherein the producingthe attenuation map includes, generating a model, and adapting the modelto an initial attenuation map, the parameterized model instance beingcreated based on the adapted model.
 21. The method of claim 13, whereinthe PET unit is configured to acquire the PET sinogram data.
 22. Themethod of claim 13, wherein a computer connected to the MR scanner andthe PET unit is configured to produce the attenuation map.
 23. Themethod of claim 13, wherein the MR scanner is configured to acquire theMR data.
 24. A non-transitory computer-readable medium, when run on acomputer, configured to instruct the computer to perform the method ofclaim
 13. 25. A device comprising: a positron emission tomography (PET)unit including a plurality of detection units and configured to acquirePET sinogram data of an object within a field of view of the PET unit; amagnetic resonance (MR) scanner configured to acquire MR data of theobject within a field of view of the MR scanner; and a computerconfigured to produce an attenuation map based on a maximum likelihoodexpectation maximization (MLEM) of a parameterized model instance andthe acquired PET sinogram and MR data, the MLEM being constrained bymodel parameters of the parameterized model instance.